Premium
Transformation to symmetry for censored data caused by a detection limit
Author(s) -
Nakamura Miguel,
DíazFrancés Eloísa
Publication year - 1994
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.3170050404
Subject(s) - skewness , transformation (genetics) , normality , quantile , symmetry (geometry) , mathematics , power transform , limit (mathematics) , statistics , normal distribution , sample (material) , scale (ratio) , function (biology) , statistical physics , econometrics , mathematical analysis , physics , geometry , biochemistry , chemistry , quantum mechanics , gene , thermodynamics , evolutionary biology , biology , consistency (knowledge bases)
Transformations to symmetry in the Box–Cox family for left‐censored observations having a common lower detection limit are considered. Recently, transformations to normality in this setting have been discussed. Symmetry, rather than normality, may be a more realistic assumption, for instance, if an estimated transformation to normality displays heavier tails than those presumed under a normal model. A method for selecting a transformation to symmetry, based on the sample skewness coefficient, is described. The advantages of transformation using this method are illustrated in a simulation study, assuming that the goal in transformation methodology is to increase precision in the estimation of the mean, quantiles, and the distribution function of the variable in its original scale. An example regarding censored measurements in polluted water samples is provided.